Figure REF  shows the basic idea of the dynamic watermarking approach. A small, secret watermark signal \(\mathbf {e}[k] \in \mathbb {R}^{N}\)  is superposed upon the IBRs' setpoints \(\Delta \omega _{\text{s}}\)  at each time step \(k\) . The watermark signal possesses some known statistics, e.g. \(\mathbf {e}[k] \sim \mathcal {N}(0, \Sigma )\)  where matrix \(\Sigma \)  is the covariance matrix of \(\mathbf {e}[k]\) . The watermark \(\mathbf {e}[k]\)  impacts the measurement of \(\Delta \mathbf {P}_{\text{G}}\) . As a result, an authentic measurement of \(\Delta \mathbf {P}_{\text{G}}\)  should reflect the statistical properties concerning the watermark \(\mathbf {e}[k]\) . By subjecting the measurements of \(\Delta \mathbf {P}_{\text{G}}\)  to certain statistical tests, a wide range of cyber attacks on the measurement of \(\Delta \mathbf {P}_{\text{G}}\)  can be detected [1]}, [2]}.
